This is an application-driven proposal that focuses on providing new insight into the molecular mechanisms of RNA catalysis through use of state-of-the-art theoretical methods. To achieve this goal, a multi-faceted approach is taken that combines quantum chemistry, molecular simulation and statistical mechanical methods, many of which have been the development focus of the initial NIH funding period. These methods are collectively referred to as "multi-scale" models for RNA catalysis: integrated methods that, when used collectively, are able to simultaneously span the broad range of spatial and temporal domains required to provide a deeper understanding of the molecular mechanisms of ribozymes. Continued development and extension of these methods plays a strong role in this renewal proposal, including the design of new semiempirical quantum models for phosphoryl transfer reactions, extension and enhancement of linear- scaling electrostatic and electronic structure methods for QM/MM simulations, and improved models for treatment of solvation and generalized macromolecular solvent boundary potential and response. Nonetheless, the main priority is to apply the recently developed methods already available to problems of phosphoryl transfer reactions that occur in solution and in ribozymes. For this purpose, we propose to calibrate and validate the new multi-scale models against important non-enzymatic reactions that have been studied experimentally, and then apply them to a focused set of three prototype ribozyme systems: the hammerhead, hairpin and hepatitis delta virus ribozymes. These ribozymes have been extensively studied by experiment (including structural information at different stages of catalysis), and offer highly complementary features in terms of their alternate catalytic mechanisms. Study of these systems in concert allows deeper insight into which features are conserved and which features might be exploited in the engineering of new ribozymes that may have considerable promise in biomedical research, the design of therapeutics, or development of new bio/nanotechnology.